Do trusting ocelots despawn?

I've finally found a jungle in my world, and spotted a couple of ocelots that I would like to bring back to my base. I've gained their trust since I've fed them with raw fish.

However, they're still ambient, passive mobs. Will they despawn after a while? Do I need to name them with a name tag?

Solution 1:

I just spawned a bunch of ocelots, tamed some of them, ran /say @e, flew >128 blocks upwards (because mobs that can despawn will instantly despawn when more than 128 blocks away from all players) and ran /say @e again. The second time I got much less output, but still some ocelots.

So the answer is: Trusting ocelots do not despawn, others do.